lim x-infty (x+sqrt{x^{2}-4x+1} =?

Question

lim x->infty (x+sqrt{x^{2}-4x+1} =?

anonymous · Answer

$$\lim_{x \rightarrow \infty} x+\sqrt{x^2-4x+1}$$ is this your question?

anonymous · Answer

yes @whatisthequestion

e.mccormick · Answer

The limit of the sums is the sum of the limits.  So you can break this up into:

$$\lim_{x \rightarrow \infty}x + \lim_{x \rightarrow \infty} \sqrt{x^2-4x+1}$$

Now, can you see the next step when you go to solve that?

anonymous · Answer

if the answer is not $$\infty $$ , i can't :/

anonymous · Answer

@e.mccormick

hartnn · Answer

the answer to this limit is actually +infinity.

anonymous · Answer

ok. thanks

e.mccormick · Answer

Yep, you got the point of breaking it up.  The x clearly goes to infinity, so the only question was if the root of the polynomial was going somewhere else faster and could change it.  But if you think about the graph of a root, it also tends towards infinity.  So it actually makes the entire thing head the same basic direction.